A recursion formula for the coefficients of entire functions which are solutions of linear differential equations with polynomial coefficients is derived. Some explicit examples are developed. The Newton sum rules for the powers of zeros of a class of entire functions are constructed in terms of Bell polynomials.
Entire solutions of ODE with polynomial coefficients, recursion formulas for coefficients, Newton sum rules for reciprocal of zeros, Bell polynomials.
MSC 2000: 65L99, 30D20, 30C10